Deflectometry is a surface slope measuring tool that requires minimal hardware and acquires surface height data with nanometer-level precision (Su, P., et al., Appl. Opt. 49(23), 4404-4412 (2010); Knauer, M., et al., Proc. SPIE 5457 366-376 (2004); and Bothe, T., et al., Proc. SPIE 5457 411-422 (2004)). It directly measures slope data, and has a very large dynamic range (P. Su et. al., “SCOTS: A reverse Hartmann test with high dynamic range for Giant Magellan Telescope primary mirror segments,” Proc. SPIE 8450, 84500W (2012)). At the most basic level, a deflectometry system must have a screen to display a pattern, and a camera to capture images of the surface (e.g., mirror, lens, etc.) under test, which is illuminated by the screen. A schematic of a deflectometry measurement setup is shown in FIG. 1 with relevant distances for use, in this example, with a mobile device. The camera hardware is chosen from off-the-shelf components where low signal-to-noise and fast acquisition times are desirable. The screens are also off-the-shelf, but the patterns displayed on the screens are areas of active research. To create a mapping, current deflectometry systems use display patterns such as line-scanning, binary patterns, and phase shifting (Butel, G. P., et al., Proc. SPIE 8493, 84930S (2012)). All of the prior art methods listed rely on changing the pattern with time and recording multiple images with the camera to reconstruct the optical surface under test. These methodologies cannot cope with time varying measurements because they multiplex information in the time domain. In doing this, they are limited to measurements in which the environment, or features on the surface, do not change in time.
In the field of laser interferometry, polarization to multiplex phase shifted data (Novak, M., et al., Appl. Opt. 44(32), 6861-6868 (2005); and Millerd & Wyant. U.S. Pat. No. 7,230,718 (2007)) uses spatial frequency carriers (Takeda, M. Elsevier Ind. Met., 79-99 (1990); and Sykora & P. de Groot, Proc. SPIE 8126, 812610 (2011)), and 2D grating structures (Kimbrough, B., et al., Proc. SPIE 6292 62920F (2006)). With these systems, measurements over very large path lengths and in unstable or turbulent environments are possible. However, phase shifting interferometry (PSI) requires a minimum of three phase shifted data sets (i.e., Δϕ=0, π/3, 2π/3) to reconstruct the surface under test (Schreiber & Bruning, Optical Shop Testing, Third Edition, D. Malacara, ed. (Wiley, 2007)), and an instantaneous measurement on a phase shifting deflectometry system would need to multiplex twice the amount of information than a similar phase shifting interferometry system would need to multiplex. This is because deflectometry measures slope data, which must be captured in two orthogonal directions to properly reconstruct the surface. Therefore, the direction of the slope data must also be distinguishable during data processing. For example, using the minimum number of phase shifts (three), six data sets would be needed: three for one slope direction, and three for the other orthogonal slope direction.
Fourier Transform Profilometry, a distinct metrology method from phase shifting deflectometry, can also be used to measure the phase of a displayed pattern. It has been employed extensively in the field of fringe projection (Xie, P., et al., Proc. SPIE 8200 (14), 1-8 (2011); and Yue, H., et al., Opt. and Laser Tech. 39, 1170-1175 (2007)). More recently, an instantaneous deflectometry method using FTP has also been studied and presented in the literature (Wu, Y., et. al., Opt. Eng. 55(22), 024104 (2016), and Huang, L., et al., Opt. Express 19 (13), 12809-12814 (2011)). FTP captures a single image of a fringe pattern with both x and y direction fringes and uses Fourier analysis to reconstruct the phase information from the image. The frequency spectrum is filtered and then inverse Fourier transformed, which generates a real and imaginary result. These values are then used to calculate the phase of the original object. FTP has the benefit of only requiring two pieces of information to be multiplexed because the Fourier analysis can reconstruct the phase from just a single pattern. In the most recent publication using FTP, Wu et. al. used color to multiplex the x and y fringes, which is not required by the FTP analysis, but it allowed them to reduce errors in the frequency domain due to overlapping spectra. However, as is true for all Fourier domain filtering, the exact method of filtering the frequency data is not a trivial step because the end result depends significantly on the process (17 Z. H. Zhang, Opt. and Lasers in Eng. 50, 1097-1106 (2012)).